Inflation: Slow Roll, Superhorizon Fluctuations, n_s

An interactive single-field slow-roll inflation model (reduced Planck mass $M_{\mathrm{pl}} = 1$; Mukhanov; Baumann, Cosmology). The slow-roll parameters $\epsilon = (1/2)(V'/V)^2$ and $\eta = V''/V$ give the scalar spectral index $n_s = 1 - 6 \epsilon + 2 \eta$, the tensor-to-scalar ratio $r = 16 \epsilon$ and the tensor tilt $n_t = -2 \epsilon$, with the e-fold count $N = \int V/V' \, d\phi$ and inflation ending at $\epsilon = 1$. Two potentials are offered: the quadratic $m^2 \phi^2$ ($n_s \sim 0.965$ but a large $r \sim 0.14$, now disfavoured) and the Starobinsky plateau $V \sim (1 - e^{-\sqrt{2/3} \phi})^2$ ($n_s \sim 0.965$, a tiny $r = 12/N^2$, favoured by Planck). The potential panel shows the inflaton rolling toward $\phi_{\mathrm{end}}$; the mode panel shows comoving fluctuations stretched as $\lambda_{\mathrm{phys}} = \lambda e^{N_e}$ past the nearly constant Hubble horizon and freezing superhorizon; the spectrum panel shows $P_s(k) \sim A_s (k/k_0)^{n_s-1}$ against the flat scale-invariant reference. Inflation ends at $\epsilon = 1$, the scalar tilt is $n_s \sim 0.965$ at about 57 e-folds, the Starobinsky tensor-to-scalar ratio sits far below the quadratic one, and the single-field consistency relation $r = -8 n_t$ holds exactly.